Evaluate 2sin30+5tan60sin60 2 sin ? 30 + 5 tan ? 60 sin ? 60 , leaving your answer in surd form.

Evaluate $\frac{2\sin 30+5\tan 60}{\sin 60}$, leaving your answer in surd form.

Answer Details

$\frac{2\sin 30+5\tan 60}{\sin 60}$
$\sin 30=\frac{1}{2};\tan 60=\sqrt{3};\sin 60=\frac{\sqrt{3}}{2}$
$\therefore \frac{2\sin 30+5\tan 60}{\sin 60}=\frac{2\left(\frac{1}{2}\right)+5\left(\sqrt{3}\right)}{\frac{\sqrt{3}}{2}}$
= $\frac{1+5\sqrt{3}}{\frac{\sqrt{3}}{2}}$
= $\frac{2(1+5\sqrt{3})}{\sqrt{3}}$
= $\frac{2+10\sqrt{3}}{\sqrt{3}}$
Rationalizing, we get
= $\frac{2\sqrt{3}+30}{3}$
= $\frac{2}{3}\sqrt{3}+10$